If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesiums ions, m and n respectively, are

Options

A. `1/2, 1/8`
B. `1, 1/4`
C. `1/2, 1/2`
D. `1/4, 1/8`

Answer

A

Explanation

For ccp arrangement , `Z=4`
`:.` No. of oxygen (O) atoms present `=4`
No. of octahedral voids `=4`
No. of tetrahedral voids `=2xx4=8`
No. `Al^(3+)` ions `=mxx4`
No. of `Mg^(2+)` ions `=nxx8`
The formula of mineral `=Al_(4m)Mg_(n8)O_(4)`
`4m(+3)+8n(+2)+4(-2)=0`
or `3m+4n-2=0`
or `3m+4n=2`
The possible values of m and n are `1//2` and `1//8` respectively
Substituting these values `(3xx1/2)+(4xx1/8)=2`